1 1 Suppose that the production function is Q = 20K²L² for a firm. If price per unit of labor is 5 Turkish Liras ( P, = 5TL ), price per unit of capital is 10 Turkish Liras ( Pz = 10TL ) and the financial capasity of firm for production is 600 Turkish Liras (C = 6007TL), find the amounts of K and L that minimize cost of the production for the firm.
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- Let a firm’s production function be f(K,L) = √2K1/2L1/2.a) Solve for the contingent demand functions for Kand L.b) Substitute the contingent demand functions in the total cost that you minimized in parta) to obtain the total cost function.c) Find the minimal amount of Kand Lnecessary to produce Q= 8 when v= 2 andw= 1 (with minimal possible cost).d) Suppose the price wincreases from 1 to 2. What happens to the demands for KandLand the total cost? e) Explain the difference in results between your answers to part d) in this question andthe previous question. Why do the impacts on demands and costs differ?A manufacturer named Kjell is facing the following product function.1 x = f(N, K) = 100Nº.8K0,2 The price for labor is NOK 500 per unit. The price for capital is NOK 125 per unit. a) Does the product function provide constant, increasing, or decreasing scale benefits? b) Kjell wants to produce 400 cakes at the lowest possible cost. How much labor and does he need capital? What will be the cost? c) The bank is not impressed by Kjell's production technology. He therefore receives a loan of only NOK 1,875. How many cakes can Kjell produce a maximum of NOK 1,875. d) Make a factor diagram (N, K). Note Kjell's adaptation from problem b) and c). Draw the isocost lines and the substituent template. e) A short-term strike leads to the price of labor rising to NOK 750. Kjell still has only NOK 1,875. How will Kjell change his adaptation from c)?How many cakes does he produce now? f) Kjell eventually starts making money, and wants to expand production to 650 cakes. What will be Kjell's new…Let a firm’s production function be f(K,L) = min{2K,L}.a) Solve for the contingent demand functions for Kand L.b) Substitute the contingent demand functions in the total cost that you minimized in parta) to obtain the total cost function.c) Find the minimal amount of Kand Lnecessary to produce Q= 8 when v= 2 andw= 1 (with minimal possible cost).d) Suppose the price wincreases from 1 to 2. What happens to the demands for KandLand the total cost?
- Provethatthetechnologyf(L,K)=L2+K2 exhibitsincreasingreturnstoscale. What is the formula for the average product of capital? For the total cost curve TC(q) = q3, prove the technology exhibits decreasing returns to scaleBoth capital and labor are variable inputs. Suppose the wage rate of labor is 16 (per hour) and the rental price of capital is 20 (per hour). The downward sloping smooth curves that bend in towards the origin are a firm's isoquants. The downward sloping straight lines are isocost lines. If the ferm plans to produce 20 units of output lper hour), its minimized cost is Capital slope=-0.8 (6,5.5) (4,5) (2,3) q=30 q=20 q=10 Labor O 180 O 160 O 164 O 122Suppose a Cobb-Douglas Production function is given by the function: P(L,K)=8L^0.7K^0.3Furthemore, the cost function for a facility is given by the function:C(L,K)=300L+500KSuppose the monthly production goal of this facility is to produce 20,000 items. In this problem, we will assume LL represents units of labor invested and KK represents units of capital invested, and that you can invest in tenths of units for each of these. What allocation of labor and capital will minimize total production Costs?Units of Labor LL = (Show your answer is exactly 1 decimal place)Units of Capital KK = Incorrect (Show your answer is exactly 1 decimal place)Also, what is the minimal cost to produce 20,000 units? (Use your rounded values for LL and KK from above to answer this question.)The minimal cost to produce 20,000 units is $ Hint: Your constraint equation involves the Cobb Douglas Production function, not the Cost function. When finding a relationship between LL and KK in your system of…
- 1) The Cobb-Douglas production function is y = 12 with a > 0 and 3 > 0. Show that MP₁ = ay/2₁, MP₂= By/22. What is the MRT S21? How does it vary with: (a) y: (b) 2/1. 2) Show that the cost function for a firm with the constant returns Cobb-Douglas production function y = Actis given by C(p, y) = ypip-B, where B is a function of A and a only. Derive the conditional input demands.Does the value of λ change if the budget changes from $4600 to $5600?What condition must a Cobb-Douglas production function q = cKαW β satisfy toensure that the marginal increase of production is not affected by the size of thebudget?A company manufactures two products, X and Y, and the joint-cost function of these products is given by c=x+4y where c is the total cost of producing v units of X and y units of Y Determine the marginal cost with respect to y when x=36 and y=16 b. The production function for a company's product is O-20, where is the output that results from /units of labor and & units of capital. The unit cost of labor and capital are $225 and $150, respectively. The company wants the total cost of puts to be $270,000 Find the number of units of capital and labor that maximize production
- Problem 5 The production function of COVID vaccines for firm O is given by v° = VKL. and requires at least one unit of labor L and one unit of capital K, i.e. L>1 und K > 1. a) After a year and some thorough research, the production function changes to VO = V4KL. (I) Compute the marginal products with respect to labor L and capital K for both production functions ! (II) Which company's the marginal products is/are larger ? What happened to the original level of production after a year ? (III) Do the production functions exhibit increasing, constant or decreasing returns to scale ? b) Suppose now, we compare production functions of company O that discovered the vaccine to a second company M. The production function of M is given by VM = K0.6 L0.4 (I) Compute the marginal products with respect to labor L and capital K for this pro- duction function ! (II) If both companies used the same equal amount of labor L and capital K, which of them will generate more output ? (III) If the…1/3 1/3 Farmer Joe's production function is f(x1, x2) = ", where xị is the number of pounds of lemons he uses and x2 is the number of hours he spends 1/21/2 2wi"wy3/2, where y is the squeezing them. His cost function is c(w1. w2, y) = number of units of lemonade produced. (a) If lemons cost $1 per pound, the wage rate is $1 per hour, and the price of lemonade is p, what is his marginal cost function?Consider the following cost function: C= 0.25q - 49° + 85q + 150: When output is 16 units, average cost is $ (Enter a numeric response using a real number rounded to two decimal places.) When output is 16 units, marginal cost is $ The output level where average variable cost equals marginal cost is units. 20 tv MacBook Air 80 DII F2 F3 F4 FB F10 F11 %23 $ & 3 4 5 8 { [ ン E R Y U P D F G K C V N M command option .. .. ト